Well, I got a little closer messing with it last night...
First off -- this has all been with the battery removed. I was like "Oh? I can test this without spending battery at all? Yes please." :D
Now... what I got working was: I could receive data in the puck FROM the terminal.
I could not, however, get output from the puck to show up on the terminal. At all.
I assumed maybe I had a bad soldering job or something, but when I flipped the TX/RX pin connections and in the .setup() call... I could receive terminal input!
So... both of the connections seem solid.
Then I noticed on the FT232R, it's got TX and RX lights that fire up when data transmits over the respective channel.
Nothing I did could get the lights to blink when sending output to the console. Serial1.print(), Serial1.println()... none of it seemed to trigger actual outgoing data.
I believe I tested swaping the TX/RX pins as well.
Tonight I'll grab a different FT232R and do some more testing.